The Kimura conjecture and other matters related to dipole motion has been discussed also in
[1]}, [2]}, [3]}, [4]}, [5]}, and from slightly different points of view in
[6]}, [7]}, [8]}, [9]}.
As mentioned, the analysis in the present paper leads to a new confirmation of Kimura's conjecture, although in a rather weak form:
expanding all quantities in Taylor series and keeping only the leading terms, the dynamical equations for a vortex pair
reduce to the geodesic equation in the dipole limit. See Theorem REF . It seems likely that stronger forms of the conjecture
(convergence of the trajectories, for example) can be formulated and proved, but we leave such matters for possible future investigations.
